T H E QUART ERLY JOU RN AL O F EXPERIM EN T AL PS YCH OL OG Y, 1999, 52A (2), 325±351
Mem ory Sp an for Arab ic Nu m erals an d Digit
Word s: Ev id en ce for a Lim ited -cap acity,
Visu o-sp atial Storage System
D ino Chincotta
Univ ersity of Bristol, Bristol, U.K .
G eoffrey U nderwood, K artini Abd G hani, Eliana Papadopoulou,
and M aja Wresinski
Univ ersity of Nottingham, Nottingham, U.K .
Six experiments examined the deter minants of the numeral advantage effect: the ® nding that
memor y span for Arabic numer als (1, 2, 3, etc.) is greater than for digit words (one, two, three,
etc.). T he speed of item identi® cation for numeral and digit words was unrelated to memory
span for the same items and a larger memory span for numer als per sisted under concurrent
random gener ation (Experiment 1). T he num eral advantage, however, was abolished wh en
the items wer e presented in random locations within an invisible 3 3 3 grid (Experiment 2)
and in locations on a horizontal plane that r an contrary to the natur al direction of reading
(Experiment 3). W hen the items were presented in the same location, a disr uption of the
spatial component of visuo- spatial working mem ory eliminated the numer al advantage
(Experiment 4), wh ereas interference with the visual component of the system did not
(Experiment 5). When the item s were spatially distributed in a 3 3 3 matrix, however,
neither visual nor spatial interference abolished the effect (Experiment 6). T aken together,
these ® ndings suggest that the numer al advantage effect is mediated by discrete components
in visuo-spatial working memory dedicated to the temporary storage and renewal of visual
codes and questions the assumption that the underlying mechanism s in immediate, visual
serial recall are equivalent between stimulus categories.
T he variation in sh or t-term memor y capacity across item categories is well documented.
Over a century ago, for example, Jacobs (1887) noted that m em ory span was gr eatest for
Ar abic num erals (9.3), then for letters (7.3), then for non sense syllables (6.1). S im ilarly,
Br en er (1940) foun d a difference in mem ory span between d igits (7.98), colours (7.06),
Requests for r epr ints sh ould be sent to D ino Ch incotta, Centre for the St u dy of M emory and L ear ning,
D epar tment of Experimental P sychology, U niver sity of Bristol, 8 Woodland Road, Br istol BS8 1T N , U.K .
E-mail: D ino.Ch incotta@ br istol.ac.u k
T he author s acknowledge the assistance of An na Ad lam and Chr istabel M eikle and thank Alan Baddeley, Ch ris
Jar rold, and Clair e O’M alley for their helpful comments and su ggestions. We are gr ateful to Rober t L ogie,
Ver non G r egg, and Joh n Richardson for valuable and constr uctive comments on this wor k. Some of the data
reported here wer e presen ted at the F ifth European Congr ess of Psychology, 6±11 Ju ly, 1997, D ublin, Ir eland.
q
1999 T he Exp erimental Psychology S ociety
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CHINCOTTA ET AL.
and geometric designs (5.31; see also, e.g., C ran nell & Par rish, 1957; H ayes, 1952; L op es
Cardozo, & L eopold, 1963). M iller (1956) observed that althou gh m emor y capacity varied
across stimulus typ e in ter ms of discrete un its of infor m ation, it was relatively constant
wh en measured in ter ms of chunks. Ch unking allows a gr eater nu m ber of, for exam ple,
individual letters to be recalled wh en sequ ences of items such as words or acron ym s are
recognized as for m ing fam iliar patter ns (e.g. BBC , PH D, N AT O ). F urther mor e, Br oadbent
(1975) argu ed that the absolute capacity of im mediate memor y is about three item s, an d
that m easures of span above this limit are largely a consequence of or ganizational pr ocesses. Althou gh providing a usable de® nition of wh at con stitutes a chunk has remained
elu sive (e.g. Sim on , 1974), th e notion that shor t-ter m mem ory capacity m ay be expanded
throu gh the reorganization of m aterial into m or e easily memor able chunks has been
in¯ uential in developing an un derstanding of the limitations of im mediate serial recall
(see, e.g., Baddeley, 1994).
Current theories of shor t-ter m mem or y can reasonably exp lain the variation in m emory span between th e different m aterials described above as arising from obviou s differen ces between th e categoriesÐ nam ely, word length (Baddeley, T hom son, & Bu chanan,
1975), frequency (Watkins, 1977), and lexicality (H ulm e, M augh an , & Brown, 1991).
T here are some relationships between stimulus typ es an d memor y span, however, th at
cann ot be accounted for easily in ter ms of these factor s alone. One example is the nu meral
advantage effect: the variation in visual memor y span between Ar abic nu m erals (1, 2, 3,
etc.) and digit words (one, two, three, etc.).
In a study of bilingu al digit span, Chincotta and U nderwood (1997a) found that
memor y span for Ar abic nu m erals (henceforth num erals) was gr eater than for digit words
in both the dom inant (Spanish) and less dom inant (English) langu ages. An equivalence in
reading tim e between nu m erals an d digit words wh en p erfor mance was speci® ed in
Spanish indicated that th e item s were matched in ter ms of spoken duration (or word
len gth). W hen English was the target langu age, however, digit words were read faster than
nu m erals. T he ® nding that reading tim e did n ot predict perfor m ance on the mem ory span
task thu s suggested that rehearsal rate was an unlikely mediator of the nu meral advantage
effect. T his notion was suppor ted further by the ® nding that the m em ory span advantage
for numerals over digit words persisted wh en subvocal reh earsal was prevented (see, e.g.,
Baddeley, L ewis & Vallar, 1984).
At ® rst sight, th e ® ndings of Chincotta an d U n derwood (1997a) may seem relatively
unsu rprisin g given the d ifferences in sh or t-term m em ory capacity that are noted as a
function of stimulus category. T he nu meral advan tage effect, however, discoun ted the
possible in¯ uence of two factor s that could theoretically mediate the variation in memor y
sp an between nu m erals and digit words, namely, word length (when perfor m ance was
sp eci® ed in the dom inant langu age) and semantic differences between the item s. An
alter native explanation for th e variation in m em ory span between nu m eral and digit words
is that these distinct representations of digits are processed in qu alitatively different ways.
A cognitive architecture of nu mber processin g developed by M cCloskey, Caramazza,
and Basili (1985) from dissociation studies of br ain -dam aged patients prop osed separate
prod uction and comprehension processes for nu m erals and digit words wh ich are
mediated by discrete lexical an d syntactical compon ents. T he lexical com pon ent is
involved in the processing of individ ual elements in a nu mber (e.g. 1 or one), wh ereas
THE NUMERAL ADVANTAGE EFFECT
327
the syntactical com pon ent processes the relationship between th e individual elem ents of
multi-digit num bers (e.g. 456 or four hundred and ® fty-six). For digit words, a further
distinction is m ade between the com pon ents used in comprehending or prod ucing spoken
(phon ological) or wr itten (graphemic) representations at the lexical processing level but
not the syntactic level wh ere th e processes are considered equivalent. For nu merals, no
distinction is m ade between p honemic an d gr aphem ic components. According to
M cCloskey et al. (1985), differences in the processin g of num erals and digit words m ay
occur at the com prehension/ prod uction stages and at the lexical/ syntactic levels of these
su bsystems.
T he M cCloskey et al. (1985) mod el prop oses that the numeral prod uction compon ent
is dedicated to the processing of rep resentations in wr itten form , wh ereas the verbal
compon ent han dles both gr aphem ic and phon ological representations of nu m ber. O ne
explanation for the variation in memor y span between nu merals and digit words, therefore, is that a m ore sp ecialized nu m ber processing system m ay be respon sible for the mor e
ef® cient recall of nu m erals. T he literatur e on num erical cognition de® nes a numeral as a
sym bol or a string of symbols representing a num ber. In this sense, therefore, a number
consists of nu merals in p rint for m (e.g. Ar abic or Rom an) or verbal equ ivalents (e.g.
M cCloskey et al., 1985). For the p ur pose of the present study, however, we used the
ter m s numeral to refer to Arabic num erals, and digit word to refer to the word for m.
T he qu est ion as to the factor s th at mod ulate the somewhat intriguing num eral advantage effect h as been left op en and merited closer attention for several reasons. M uch
research effort has been dedicated towards understand ing the processes that underlie
imm ediate serial recall (e.g. Bu rgess & H itch, 1992; H enson, N or ris, Page, & Baddeley,
1996). Althou gh memor y capacity varies as a function of stimulus category, it has been
assumed that the organizational m echanism s that underlie imm ediate visual serial recall
for different materials are generally equivalen t or, at least, comp arable. If this were
demon strated to be otherwise, im por tan t restriction s would be p laced on the extent to
wh ich the ® ndings of studies of m emor y span involving num erals could be generalized to
other stimuli. T his p oint becomes m or e poignant wh en on e consid ers th at nu m er als are
amon g th e most widely u sed experimental stimuli in stu dies of shor t-ter m m emor y.
F urther mor e, th e sem antic and word-length equivalen ce between nu m erals and digit
words provides an op por tunity to examine th e relationship between the visual an d verbal
compon ents of working m em ory theory.
T he working m em ory m od el or iginally developed by Baddeley and H itch (1974) an d
later mod i® ed by Baddeley (1986) consists of three compon ents: two sp ecialized slavesystems ded icated to the processing of verbal an d visual material and a third, m od alityfree, atten tional system that m on itor s inform ation processing and allocates additional
stor age and processing capacity as and wh en required.
T he system ded icated to the processin g of verbal infor m ation, the phon ological loop,
consists of two subsystems op erating in tandem . T he phon ological store passively maintains speech-based inform ation br ie¯ y wh ere it is subject to trace decay and becomes
irretrievable after app roximately 2 sec. Infor m ation is m aintained m ore or less inde® nitely
by the intervention of the dyn amic articulator y control pr ocess that refresh es the traces in
the phon ological store throu gh subvocal rehearsal. Items of shor t word len gth thus
occupy less tem por al capacity and are rehearsed subvocally at a faster rate than are longer
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CHINCOTTA ET AL.
on es. W h en th e articulator y control process is disru pted by articulator y su pp ression (the
concurren t articulation of an ir relevant phrase such as the, the, the, e.g. M ur ray, 1965),
word length ceases to be an in¯ uential deter minant of m em ory span as recall is no longer
affected by differences in articulatory duration (Baddeley et al., 1984). T he phon ological
loop is the most researched an d best un derstood system within the workin g memor y
architecture and accounts neatly for a wide range of experim ental ® ndings such as the
word-length effect (Badd eley et al., 1975) and the related cross-lingu al digit-span effect
(Chincotta & U nderwood, 1997b; N aveh-Benjamin & Ayres, 1986).
T he ® ndings of C hin cotta and U n derwood (1997a), however, ind icated that the
nu m eral advantage effect was mediated by the functioning of on e or both of the remaining
compon ents of the working m em or y m od el. Recent th eoretical developments (e.g. L ogie,
1995 ) have suggested that the com pon ent dedicated to the processing of visual infor mation (the visuo- spatial scratch pad) in working m emory is stru cturally and functionally
analogous to that of phon ological loop. Althou gh there are clear sim ilarities between these
discrete working mem ory slave systems, dissociations of visual and sp atial processing have
indicated that the visuo-sp atial scratch pad architecture is somewhat m ore complex than
that of the phon ological loop (e.g. L ogie, 1986, 1989; Quinn & M cCon nell, 1996).
T he central executive plays a part in the transfor m ation of infor m ation into mor e
ef® cient codes such as chunks (Badd eley & H itch, 1974). T he task of concurrent random
generation has been found to overload the central executive an d disrupt its nor m al functioning and is, thus, an approp riate means of exam in ing central execu tive functioning
within the working m em ory mod el (e.g. Baddeley, 1996). T he requirement of generating
random letter strings, for exam ple, elicits a sequenced alphabet schema that con¯ icts with
the requirem ent of keeping the ou tput sequence random (in the case of verbal random
generation, of course, phon ological loop functioning is also disr upted). U n der these circu mstances th e role of the central executive is twofold: it assists the selection of str ategies
involved in the generation of item s an d simultaneou sly m on itor s the ou tput to ensure that
it is su f® ciently random (see, e.g., Baddeley, Emslie, K olodny, & D u ncan, 1998).
So, in theoretical ter ms, what factor s independen t of speech rate could contribute
toward the m emor y span advantage for num er als over digit words? T h ere is evidence
that the speed with wh ich items are recognized is on e in¯ uen tial deter m inant of memor y
sp an. M ackworth (1963), for example, dem on strated that nam ing speed predicted the
memor y span relationship between nu merals, words, and pictures, with a larger span for
the item s with faster nam ing latencies. In addition, D em pster (1981) su ggested that item
identi® cation is the m ajor source of in dividual d ifferences in m emor y span and that the
word length effect (Baddeley et al., 1975) may be accounted for in ter m s of variation in
item identi® cation, with faster respon se latencies for shor t than for long words. K ail
(1992) h as argu ed that processing speed m akes an independent contribution to subvocal
rehearsal, wh ich, in tur n, d eter mines m em ory span. T his view holds that a shor ter
respon se latency allows add ition al tim e for the encoding an d organization of m aterial
prior to recall. T hus, wh en the availability of processing tim e is depen dent upon tem por al
constraints im posed by lim ited presentation tim e, as in m em ory sp an tasks, item identi® cation tim e is a variable of som e consequence.
H itch, H alliday, and L ittler (1989), however, found that auditory and visual respon se
latencies cor related with m emory span on ly wh en this was measured u nder articu lator y
THE NUMERAL ADVANTAGE EFFECT
329
su pp ression. U nd er silent recall conditions, articulation tim e and reading tim e were
equivalen tly correlated with memor y sp an . Reading time was also cor related with suppressed memor y span, althou gh the degree of association between this predictor an d
visual item identi® cation was different. T hese ® ndings thu s suggested that the relationsh ip between item identi® cation and memor y span was not as straightforward as had been
su ggested by D em pster (1981) and K ail (1992).
In ter ms of the presen t interest in the nu meral advantage effect, h owever, it shou ld be
noted th at the above-cited studies rep or ted a shor ter respon se latency and larger memor y
sp an for nu m erals in relation to arbitrary words rather than digit words. N evertheless, the
evidence suggested that variation in the speed with wh ich num er als and digit words are
identi® ed could be on e im por tant variable in m ed iating the differential memor y span
between the items.
Chincotta and U nderwood (1997a) prop osed that an alter native explanation of th e
nu m eral advantage effect lay in a difference in th e way the two sets of items were
organized prior to prod uction. T hey reasoned that sequences of digits are encoun tered
mor e often in nu m eral than digit word for m (e.g. 9 5 1 5 2 8 2 as op p osed to nine ® v e one
® v e two eight two) and that more established associations between num erals and digit
words m ay have been the critical variable affecting the patter n of m emor y span.
As described above, chun king entails the recod ing of discrete items (e.g. 7, 5, 3) into a
single unit (i.e. 753) and engenders econom ies in processing by integrating discrete items
of infor mation into larger units using fam iliar patter ns stored in long- ter m m emory.
Con sequently, m em ory span is increased dramatically by expanding the nu m ber of items
within a ch un k. T he ben e® t of a high degree of familiarity with juxtapositions of nu m erals, such as running tim es, has been dem on strated in stud ies of mnem on ists (Ericsson &
Chase, 1982). It seem s plausible, therefore, that a difference in th e d egree of fam iliarity
with wh ich the distinct representations of digits are encountered m ay occasion a bias in
favour of additional suppor t for num erals relative to digit words in memor y span tasks.
Chincotta and U nderwood (1997a) posited that a higher degr ee of familiarity with
sequences of digits in num eral for m may h ave resulted in a bias in favour of nu m erals
toward s a gr eater ef® ciency in recoding sequences into chunks throu gh the u se of mnemon ic strategy. T his view, then, h olds that the numeral advantage effect is m ediated by a
putative d ifference in the strength of associative relationships between num erals on the
on e hand an d digit words on the other rather than an overall variation in frequency
between each stimulus category.
EXPERIMENT 1
T he ® rst experim ent tested the involvement of two factor s that could account for the
variation in m emor y sp an between the different representations of d igits. F irst, we examined the relationship between item id enti® cation and mem or y span for nu merals and digit
words. If respon se latency in item identi® cation is negatively associated with perfor mance
on the m emor y span task, it wou ld be reasonable to conclude th at this factor was on e
in¯ uential deter m in an t of the num eral advantage effect. S econd, we examined wh ether
the cen tral executive and attention-demanding processes related to chunking are implicated in mediating the superior m em or y span perfor mance for nu merals over digit words
330
CHINCOTTA ET AL.
by m easurin g m em ory span for these items u nder random gener ation . If a difference in
the predisposition for strategically organizin g m aterial into chunks between the item s is
an in¯ u ential deter minant of the nu m eral advantage effect, a secondary task that disrupts
central executive functioning shou ld eliminate the difference in memor y span between
nu m erals and digit words.
Method
Subjects
T he subjects were 24 (11 female, 13 male) undergraduate and postgr aduate students registered
with a British univer sity; they were paid for par ticipation.
Materials
For the item identi® cation task, 72 digit pair s (1±9) were constr ucted. H alf of the digit pairs (36)
were constructed at random, subject to the following restrictions. Each digit occur red 8 times (4
times in the ® r st position of the digit pair and 4 times in the second) and the items in each pair were
different (e.g. 3±7, 4±2, etc.). T he remaining digit pairs consisted of four pairings for each of the
digits from 1 to 9 (e.g. 1± 1, 2± 2, 3± 3 etc.). T he digits were recorded digitally by a female and edited
using SoundEdit Pro (M acrom ind). A com puter presented the ® r st item from each digit pair
aud itorily, and the second item was presented visually in the same location on the screen. For
both the same and different pairings, 4 of the visually presented items occur red as numerals and 4
were presented as digit words.
For the measurement of memory span, 6 sets of random digit sequences (1±9) were constr ucted.
Identical items appearing contiguously and ascending and descending sequences (e.g. 3, 4, 5 and 8, 7,
6) were avoided. After two sequences of the initial length, the number of items increased by one, and
so on. T hr ee sets comprised Arabic numerals, and the rem aining sets consisted of digit words. For
the control condition, the sequences commenced with an initial length of three items, whereas in the
remaining recall conditions, the sequences commenced with an initial length of one item.
Procedure
F irst, the subjects completed the item identi® cation task. T hey were required to decide wh ether
the digit pairs were the same or different by pr essing appropriately labelled keys on a computer
keyboard. Before testing, the subjects were given a pr actice consisting of 9 digit pair s. T he presentation of the digit pairs was random ized by com puter. T he presentation sequence was as follows. F irst,
a rhombus prompted the subjects to press the space bar on a computer keyboard. A ® xation point
app eared (1 sec) followed by a blank screen (1 sec), after wh ich the ® rst item was presented auditorily
via loudspeakers. T he second item was presented visually 250 msec after the onset of the ® r st. T he
period between the onset of the second item and the response was taken as a measure of item
identi® cation.
N ext, the subjects perfor m ed the m em or y span task. T he subjects were ® rst shown two examples
of a presentation sequence. T hen the articulatory suppression task was introduced, and the subjects
practised repeating the phrase la± la continuously at the rate of one phr ase per second in time to a
metronome. Two pr actice memory span trails involving articulatory suppression were then presented. N ext, the subjects were introduced to the random generation task and asked to imagine a
hat containing the letters of the alphabet from wh ich letters were selected at random , articulated, and
THE NUMERAL ADVANTAGE EFFECT
331
replaced. T he subjects were reminded that it would be improbable that words, acronyms (e.g. NAT O or
BBC ), and regular sequences (e.g. ABC or XYZ ) would occur. T he subjects then completed two practice
trials involving the r andom production of approximately 20 letters at the r ate of one item per second
placed by a metronom e.
T he sequences were presented visually at the rate of one item per second, and each successive
item appeared in the same position on the monitor. T he presentation sequence was as follows. F irst,
the legend READ Y appeared and prom pted the subjects to press the space bar, after wh ich a blank
screen appeared for 500 m sec, followed by a ® xation point (500 msec) and the item sequence. When
the item sequence ter minated, a blank screen appeared for 2 sec, followed by the legend RE CAL L ,
wh ich prompted the subjects to commence verbal recall. For the measurement of memory span
under ar ticulator y suppression and concurrent random gener ation, the legend L A±L A or L ETT ERS, respectively, appeared on the screen 1 sec after the sequence was initiated and remained
visible for 2 sec. T his prom pted the subjects to commence articulatory suppression or r andom
gener ation, respectively.
For all three conditions, recall was thus pr om pted 2 sec after presentation of the last item. For the
articulatory suppression and random gener ation conditions, commencement of the secondary task
was signalled 4.5 sec prior to the presentation of the item sequence and ensured that the secondary
tasks commenced before the item sequences were presented.
T esting continued until the subject recalled both sequences of the same length incor rectly.
M emory span was operationalized as the length of the last cor rectly recalled sequence. If both
attempts at the last correctly recalled sequence length were successful, a bonus of 0.5 was added
to the memory span score. Condition order and practice were counterbalanced by a L atin
square.
Results
Incor rect respon ses from the item identi® cation task (less than 0.5% ) were excluded from
further analysis. T he rem ainin g d ata were averaged and subm itted to a two-way analysis
of variance (AN OVA) in wh ich item (numerals or digit words) and pairing (same or
different) were within-subjects factor s (see F igure 1). T h is indicated reliable m ain effects
of item , F(1, 23) = 33.96, p < .0001, with a shor ter response laten cy for nu m erals
(609 msec) than d igit words (664 m sec), and pairing, F(1, 23) = 68.38, p < .0001, with
a shor ter respon se latency for identical item s (597 msec) than different (677 msec) items.
T he interaction between the factor s was not reliable, F(1, 23) < 1. T he results of the
cross-mod al m atching task th us indicated that respon se latency was shorter for nu m erals
than for digit words an d that identical pairs were identi® ed faster than were different
pairs.
T he data from the m emory span task were subjected to a two-way AN OVA in wh ich
item (numerals or digit words), and condition (control, articu lator y su ppression, or random gen eration) were within-subjects factor s (see F igure 2). T his in dicated a reliable
main effect of item, F(1, 23) = 23.10, p < .0001, with a larger span for numerals (5.35)
than digit words (4.73). T h e main effect of condition was also reliable, F(2, 46) = 164.34,
p < .0001. F u rth er analysis by t-test indicated that the m ean s for each recall con dition
(silent = 6.56, articulator y suppression = 5.39, random generation = 3.20) differed
amon gst themselves (all t > 5, p < .001). T he interaction between the factor s was not
reliable, F(2, 46) = 1.58. T he results of the m emory span task thus showed th at memor y
FIG. 1.
M ean respon se latency (msec) in the cross- modal matching task for same and differ ent digit pairs in
Experiment 1. T he error bar s represen t st andard deviations.
FIG. 2.
M ean memor y span for nu mer als and digit wor ds u nd er silent, articulatory su ppr ession, and concur rent r andom gen eration con ditions in Experim ent 2. T he err or bar s represent st and ard deviation s.
332
THE NUMERAL ADVANTAGE EFFECT
333
sp an for num erals was larger th an for d igit words and that n either articulator y suppression n or random generation secondary tasks abolished the numeral advantage effect.
A series of Pearson cor relations was perfor m ed on the data to exam ine the relationship
between the m ean item iden ti® cation m easures and numeral and digit word span across
recall conditions (see T able 1). T he results of the cor relational analysis indicated that
respon se latency on the cross-m od al m atch ing task was not reliably correlated with the
memor y span measures. T he cor relation between mean item identi® cation time and overall mean m emor y span was also not reliable (2 0.27). T his ® n ding su ggests that th e
nu m eral advantage effect is not m ed iated by a faster speed of percep tual processing for
nu m erals in relation to digit words.
Discussion
Respon se latency for num erals was shor ter than for digit words, and a mem ory span
advantage for num erals was n oted under all conditions. T he shor ter respon se latency
noted for num erals than digit words provides an initial suggestion that the variation in
perfor mance is m ediated by a higher frequ ency for nu m erals, as faster respon ses are
nor mally associated with high-frequency rather than low-frequency items (see, e.g.,
Ru benstein, G ar® eld, & M illikan, 1970). T h e absence of a relationship between respon se
latency and m emor y span, however, suggests that the nu meral advantage effect is not
sim ply mod erated by a shor ter identi® cation time for numerals than digit words. W hilst
the possibility th at the lack of a signi® cant cor relation was sim ply a re¯ ection of the small
sam ple size could not be discounted at this stage, the following experiment was designed
partly to address this issue.
T he persistence of a superior mem or y span for nu merals under articulatory suppression con® r m s that the variation in mem or y span between the stimuli is not mediated by
the phonological loop. T he ® ndings also discount an explanation of th e nu m eral advantage
in ter ms of a variation in the predisposition with wh ich num erals and digit words may be
integrated in to ``chunk- like’ ’ units and the explicit use of m nemon ic system s, because if
this were the case, the disruption of th e central executive by the random generation task
sh ou ld have abolished the nu m eral advantage effect (Badd eley & H itch, 1974).
As discussed above, however, Chincott a and U nderwood (1997a), prop osed that a
difference in the strength of associative connections between num erals and digit words
(occasioned by a greater exposure to sequ ences of nu m erals, e.g. telephon e nu mbers,
TABLE 1
Correlations between Response Latency and Memory Span for
Numerals and Digit Words in Experiment 1
Condition
N umerals
D igit word s
df = 22
Control
Articulatory Suppression
Random G eneration
2 0.14
2 0.33
2 0.26
2 0.26
2 0.10
2 0.27
334
CHINCOTTA ET AL.
personal identity nu m ber s, cricket scores, etc.) rather th an individual variation in frequ ency between items could be a critical m ediator of th e num eral advantage effect. T he
persistence of a larger m em ory span u nder r an dom generation suggests that the effect is
unlikely to be occasioned by an explicit, strategic advan tage for nu merals. An alter native
view, however, is that increased exposure to num eral strings may have occasioned a mor e
ef® cient, as yet u nspeci® ed, im plicit for m of processing within the working memor y
system. If this were the case, this could explain wh y the num eral advantage effect was
imperviou s to in terference from the rand om generation as such secondary tasks are unlikely to disrupt processes that are high ly autom atized or im plicit in nature.
EXPERIMENT 2
T he next experim ent examined the effect of a pu tative variation in the strength of
associative visual connections between num erals and digit words in m ediating the nu meral
advantage effect. A d isruption of th e visuo-spatial links between the stimuli was achieved
by m anipulating the location in wh ich item s were presented within an invisible 3 3 3 gr id.
In an ordered condition, the initial item was p resented in the top left-hand cell, an d the
order of presentation then proceeded from left-to-right and row by row from top to
bottom . In a random condition, the items appeared within the sam e visual area, bu t the
stimulus location was unpredictable.
T his manipulation thu s contrasted a condition in wh ich th e location of stimuli was
predictable and wh ich maxim ized the strength of possible associative connections between
them with on e in wh ich location was unpred ictable and min im ized the degree to wh ich
prior exposure to nu m erals could be advantageous in suppor ting mem ory p erfor mance.
Random presen tation was expected to interfere with the nor mal patter n of p rocessing an d
thereby provide some indication as to wh ether a difference in exposure to digit strings
between num erals and digit words was an im por tant factor in mediating the differential
memor y sp an s for these items. In addition, the p resent design further examined the
notion of wh ether the numeral advantage effect was a consequen ce of a higher degree
of familiarity (or sh or ter identi® cation time) for nu merals than words. If this were the
case, a larger mem or y span for nu m erals shou ld be n oted under both or dered and random
presentation conditions.
Method
Subjects
A total of 20 science undergraduates (10 female, 10 male) registered at a British U niver sity were
paid for participation.
Materials and Procedure
For the measurement of mem ory span, 4 sets of r andom digit sequences were constructed, as
descr ibed for Experiment 1. T he sequences commenced with an initial sequence length of three
items. After four presentations at this length the number of items increased by one, and so on to a
maximum of 12 digits. Two of the sets consisted of Ar abic numer als and two comprised digit words.
THE NUMERAL ADVANTAGE EFFECT
335
T he sequences were presented visually via a com puter monitor at the r ate of 1 item per sec (each
item remained visible for 1 sec) within an area m easur ing approximately 12 3 9 cm. T his area was
subdivided into an invisible 3 3 3 m atrix. In the ordered condition, the initial item of each sequence
app eared in the top left-hand cell in the grid. T he presentation sequence then proceeded from left to
right, row-by-row, and from top to bottom. If a mem ory span of 9 items was exceeded, in the ordered
condition the presentation cycle recommenced; in the random condition, the location of items within
the matrix was unpredictable subject to the constraint that adjacent items in the sequence were not
presented in the sam e cell or adjoining cells on the same row.
T he presentation sequence was as follows. F irst, the legend RE AD Y appeared and prompted the
subjects to press the space bar, after wh ich a blank screen appeared for 500 msec, followed by a
® xation point (500 msec) and the item sequence. W hen the item sequence ter minated, a blank screen
app eared (500 msec) followed by the legend RECAL L (1 sec), wh ich prompted the subjects to
commence spoken recall.
Before testing, subjects were allowed practice on two 3-item sequences under both ordered and
random presentation. T esting continued until all attem pts at the same sequence length were incorrect. A score of 0.25 was added to the memory span score for each correct response at the last
correctly r ecalled sequence length. All other procedural details were as described for Experiment 1.
Results
T he memor y span data were subjected to a two-way AN OVA in wh ich item (num erals or
digit words) and condition (ordered or ran dom ) were within-subjects factor s (see F igure
3). T he m ain effect of item was not reliable, F(1, 19) < 1, bu t th e m ain effect of con dition
was, F(1, 19) = 6.60, p < .05, with a larger memor y span for ordered th an for random
presentation (means = 7.75 and 7.21, respectively). T he interaction between the factor s
was also reliable, F(1, 19) = 12.04, p < .01.
An alysis of the interaction by sim ple m ain effects indicated that the differen ce between
nu m eral and digit word span was reliable in the ordered presentation condition, F (1, 19)
= 4.99, p < .05 (m eans = 7.98 and 7.53, respectively), bu t not for random presentation,
F(1, 19) = 1.46 (m eans = 7.09 and 7.34, respectively). T he difference between ord ered
and ran dom presentation was reliable for nu m erals, F(1, 19) = 10.08, p < .01 (means =
7.98 and 7.09, respectively), bu t no correspon din g difference was noted for digit words,
F(1, 19) < 1 (m eans = 7.53 and 7.34, respectively), hence the interaction ter m .
Discussion
W hen the presentation of stimuli followed a predictable sequence of spatial locations,
memor y sp an for num er als was larger than that for digit words, however, wh en the items
were presented in random locations within the sam e visual area, n o difference was noted
between nu merals and digit words. T hese ® n dings strikingly demon strate that a presentation condition that disrupts the patter n in wh ich numeral strings are typ ically experien ced abolishes th e superior memor y span for num erals in relation to digit words.
M or eover, random presentation occasioned a decrem ent in mem ory span for nu m erals,
wh ereas digit word span was unaffected by presentation cond ition. T he decrem ent in
nu m eral span could, thu s, n ot be attributed to an increased level of dif® culty in this task
compared to ordered presentation, for, had th is been the case, random presentation would
336
CHINCOTTA ET AL.
FIG. 3.
M ean memory sp an for numerals and d igit words un der order ed and r andom pr esentation conditions
in Experiment 2. T he error bar s repr esent standard deviations.
have occasioned a sim ilar reduction in digit word span. Instead, th is ® nd ing suggests that
random distribution speci® cally affects perfor mance for num erals. In addition, the ® nding
that a num eral advantage was noted on ly under or dered presentation fu rth er discounts
the notion that the numeral advantage effect is a consequence of greater fam iliarity or
faster item identi® cation for in dividual nu merals than for words. Were th is the case, then a
larger m emor y span shou ld h ave been n oted for nu m erals und er both ordered and random presentation conditions.
EXPERIMENT 3
It could not be established from the results of Exp eriment 2 wh ether the decrement in
nu m eral sp an under random presentation was occasioned by factor s related to visu al
search or a disru ption of the familiar visu o- spatial patter n in wh ich num erals are nor mally
en countered . T he next experim ent, therefore, addressed this potential confou nd an d
exam ined in closer detail wh ether the disruptive effect of random pr esentation on m emory perfor mance for num erals was occasioned by the unpredictability of presentation
location or a mor e speci® c consequence related to the disruption of the visuo-spatial
stor age m echanism. T his was achieved by presenting the stimuli across a horizontal plane
divided into nine equidistant locations: a procedure similar to that used by H itch an d
M or ton (1975) in an examination of spatial and tem por al factor s in serial recall. In on e
condition, the ® rst item was presented in the right-most location on the plane, an d
presentation pr oceeded sequen tially from right to left (R±L ), wh ereas in a second con-
THE NUMERAL ADVANTAGE EFFECT
337
dition the initial item was presented in the left-most location on the plane and proceeded
from left to right (L ±R). In contrast to Exp eriment 2, therefore, the present d esign
allowed the location of the item s in the sequence to be pred ictable in both presen tation
conditions.
T o maximize the contrast between the presentation directions, we tested H ebrew sp eakers and exploited a distinctive feature of the H ebrew langu age. In H ebrew, th e reading of
printed text is from right to left. W hen a multi-digit item in Ar abic nu m eral for m (e.g.
1997 ) is encou ntered, however, the direction of parsing switches to left-to- right. W hen the
processing of the nu m eral string is com pleted, a right-t o-left direction is resumed.
If the decrement in m em ory span for num erals under random presentation noted in
Exp eriment 2 was occasioned solely by th e un predictability of the location at wh ich items
were p resented, a nu meral advan tage effect shou ld be noted under both L ±R and R±L
presentation, as, und er these circumstances, th e item sequence was pred ictable in each
case. If, on the other hand, an established patter n of associative visual links was crucial in
mediatin g the nu m eral advantage, a predictable bu t unfam iliar presentation direction
sh ou ld diminish the extent to wh ich prior experience would suppor t perfor mance. U nder
these circu mstan ces, m em or y span for nu merals shou ld be gr eater under L ±R than under
R±L presentation.
Method
Subjects
T he subjects were 12 (5 fem ale, 7 m ale,) university students registered with a university in T elAviv, Isr ael. All the subjects were native H ebr ew- speaker s wh o had been educated exclusively in
H ebrew; they volunteer ed for participation.
Materials and Procedure
Four new sets of digit sequences were prepared according to the criteria speci® ed for Experiment
1. T he sequences com menced with an initial length of three item s, wh ich was incremented by one
item after four presentations to a maximum of 12 item s. Two of the sets consisted of Ar abic num er als,
and the remaining two comprised H ebrew digit words. T he items were presented on a horizontal axis
running across the centre of a com puter monitor. T his imaginary line was divided into nine equidistant locations in wh ich the items were presented. Presentation of the sequences was blocked
according to item and condition (left-to-r ight or r ight-to-left). All other procedur al details were
identical to those described for Experiment 2.
Results
T he m em ory span data were subjected to a two-way AN OVA in wh ich item (num erals
or digit words) and condition (L ±R or R±L ) were both with in-subjects factor s (see F igure
4). T he m ain effect of condition was not reliable, F(1, 11) < 1, bu t the m ain effect of item
was, F(1, 11) = 9.58, p < .05, with a larger m emor y span for nu merals than for digit
words (m eans = 7.18 and 6.75, resp ectively). T he interaction between the factor s was also
reliable, F(1, 11) = 11.30, p < .01.
338
CHINCOTTA ET AL.
FIG. 4.
M ean memory sp an for nu merals and digit words un der right to left (R±L ) and left to right (L ±R)
pr esentation in Experiment 3. T he error bar s r epresen t standard deviations.
An alysis of the interaction by simple main effects ind icated a d ifference in memor y
sp an as a function of presentation direction for nu m erals, F(1, 11) = 20.81, p < .001, with
a larger span for L ±R than for R±L presentation (means = 7.63 and 6.73, respectively). A
correspon ding d ifference was noted for digit words, F (1, 11) = 11.52, p < .01; however,
in this case a larger m em ory span was noted for R±L than for L ±R presentation (means =
7.08 and 6.42, respectively). N um eral sp an was greater than digit word span for L ±R
presentation, F(1, 11) = 38.35, p < .0001, wh ereas the difference in m em ory span
between item s for R±L presentation was m arginal, F(1, 11) = 3.29.
T he relationsh ip between nu meral and digit word span u nder op timal (i.e. L ±R for
nu m erals and R±L for digit words) and non -op timal (i.e. R±L for numerals and L ±R
for digit words) presentation directions was exam ined by a two-tailed t-t est. T his indicated a larger m emor y span for num erals than for digit words for the op tim al direction
of presentation, t(1, 11) = 3.03, p < .05, wh ereas no difference between the items was
noted u nder non -op tim al presentation, t(1, 11) = 1.48.
Discussion
T he ® n dings of Exp eriment 3 indicate that m em ory span for nu m erals was greater under
L ±R than R±L presentation, wh ereas for digit words this patter n was reversed an d a larger
memor y span under R±L than L ±R presentation was noted . M emor y span is, thus, gr eater
wh en the direction of presentation follows the natural read ing patter n in H ebrew for each
stimulus. In addition, the num eral advantage under op tim al presentation for each item
THE NUMERAL ADVANTAGE EFFECT
339
indicates that num er als enjoy an add ition al source of suppor t in memor y span tasks that is
unavailable for digit words. It is of some interest to note that the presentation of items in
ordered gr id and fam iliar hor izontal for m ations is bene® cial in im proving m em ory sp an for
both nu merals and digit words. Com pare, for exam ple, the mean con trol nu meral span in
Exp eriment 1 (6.8) with that of ord ered p resentation in Exp eriment 2 (7.98) and L ±R
presentation in Exp eriment 3 (7.63). T his suggests that there is something about presentation for mats in wh ich material is distributed in predictable and familiar patter ns that
provides additional supplementary cues that lead to im proved overall perform ance.
In Exp erim ent 2, no difference in d igit word span was noted between or dered an d
random presentation. By contrast, an effect of scanning direction was noted in Exp eriment 3, such that digit word span was gr eater und er R±L than L ±R presentation. T hese
® ndings indicate that memor y span for d igit words is sensitive to the direction of presentation along a hor izontal axis, wh ereas it rem ains unaffected by presentation order
within a 3 3 3 matrix. Alth ou gh further investigation is required before a d etailed
account of the differential effect of presentation location/ direction for digit word s in
Exp eriments 2 and 3 may be arrived at, it has been suggested that the elliptical nature
of th e hum an visual ® eld is advantageously predisposed to the processing of infor m ation
along horizon tal plan es (see, e.g., H oosain, 1991; H oosain & Poon, 1997). T h is possibility
provides a plau sible explanation of the differen t effects of presentation location on digit
word m emor y span between Exp erim ents 2 and 3.
T he ® ndings presented so far indicate that neither articulator y suppression nor random
generation impact upon the num eral advan tage effect. Random location (Exp eriment 2) and
unfamiliar p resentation direction (Experiment 3), however, are two experimental manipulations that abolish the m emor y span advantage for num erals over digit words. T aken
together, th ese ® ndings seem to sup por t the view that the decrement in nu m er al span under
random presentation (Exp erim ent 2) is occasioned by a disruption of the established visual
patter ns in wh ich nu meral stimuli are nor mally encountered, rather than the unpred ictability of presentation location. Althou gh these results could be taken to indicate that spatial
inform ation is a cru cial factor in m ed iating the nu meral advantage, th e ® nd ing of a nu meral
advantage wh en the items were presented in the same location (Exp eriment 1) raises questions about the relevance of the spatial familiarity hyp othesis. W hat is it about r andom and
unfamiliar sp atial distributions, then, that elim inates the num eral advantage?
Idzikowski, Baddeley, D im bleby, and Park (1983, see also Baddeley, 1983) showed that
the voluntary eye m ovements involved in tracking a visual target disrup ted spatial pr ocessing, wh ereas no disruption was noted under conditions in wh ich involuntary eye m ovements were in duced or the eyes rem ained stationary and ® xated on a moving visual ® eld.
A fu rth er, related, demon str ation of the disruptive effect of eye m ovements on visual
processing may be found in the work of Byr ne (1972). H e dem on strated that a respon se
for mat that was incom patible with the direction in wh ich visu al infor m ation was presented occasioned a decrement in perform ance com pared to a condition in wh ich the
direction of respon se was consistent with that of presentation. In addition, An drade,
K avanagh, and Badd eley (1997) found that both eye movem ents and complex (boustrophedon ) spatial tapping disr upted the vivid ness of visual imagery.
T aken together, this evidence suggested that spatial tapping an d eye m ovements make
sim ilar demands on visuo- spatial working m em or y. If th is is so, then on e explanation for
340
CHINCOTTA ET AL.
the elimination of a nu m eral advantage under rand om presentation (Exp erim ent 2) is that
this is occasioned by a disrup tion of visuo- spatial m emor y throu gh eye movem ents rather
than a disruption of established visual associations between num erals. F urtherm ore, if a
presentation direction contrary to the established patter n of reading is regarded as comprising an element of incom patibility between presentation and natural expectations in
processing, this provides a plausible explan ation for the ® nding of a numeral advantage
under op tim al scanning directions for nu merals and digit words an d the elimination of the
difference under non -op tim al presen tation (Exp erim ent 3). A logical next step, therefore,
was to examine in greater detail the involvem ent of visuo-spatial working memor y in
mediatin g the num eral advan tage effect.
In a mod i® ed mod el of the visuo-spatial sketch pad, L ogie (1995) prop osed that this
compon ent of workin g m em ory consists of tem por ary visual and spatial systems into wh ich
inform ation gains access via long- ter m m emory representations of the material bein g
processed. Entry into either the p assive visual store (the visual cache) or the dyn amic
sp atial rehearsal system (in ner scribe) is depen den t upon the nature of the infor mation that
is activated. T he traces in the visual store are subject to both decay and interference from
new infor mation but can be refreshed by the action of the spatial rehearsal system. In
addition to provid ing a rehear sal-like renewal or regeneration of fading activations, the
sp atial store extracts inform ation for the planning and execution of m ovement.
T asks th at require subjects to tap p re-speci® ed spatial sequences concurrently (spatial
tapping) have been d em on strated to interfere selectively with m easures of spatial span
su ch as the Cor si task (e.g. Smyth, Pearson, & Pendleton , 1988; Smyth & Pendleton ,
1989 ) and affect the solution of spatial bu t not verbal problem s (F ar mer, Ber man, &
F letch er, 1986). T he effects of spatial tapping on spatial processing are akin to the effects
of articulatory suppression on verbal processing (S myth & Pelky, 1992).
EXPERIMENT 4
In Exp erim ent 4, the role of visuo-spatial working memor y in m ediating the num eral
advantage effect was examined by m easurin g the effect of a secondary task that disrupts
the spatial reh earsal system on m emor y span for nu m erals an d digit words. M easures were
obtained under control, articulator y suppression, and sp atial tapping conditions, and the
item s were p resented in th e same location.
Method
Subjects
T he subjects wer e 36 (28 female, 8 m ale) univer sity students, registered with the same university
in the U nited K ingdom, wh o volunteered for par ticipation.
Materials and Procedure
T he materials and procedure were identical to those described for the memory span task in
Experiment 1, with the following exceptions. In Experiment 4, three trials at each sequence length
were pr esented. For the measurement of memory span under spatial tapping, a wooden board (15 cm
THE NUMERAL ADVANTAGE EFFECT
341
square) with cylindrical wooden pegs (1.5 cm high and 1.5 cm in diameter) in each cor ner was
constructed. T he board was placed approximately 50 cm either to the right or to the left of the
subject and was, thus, only peripherally visible wh en the subject attended to the screen. T he subjects
were required to tap the pegs individually in a clockwise direction with the preferred hand at the r ate
of one tap per 500 m sec in time to a metr onome. Befor e testing, the subjects were allowed two
practice trials under spatial tapping. A score of 0.33 was added to the m emory span score for each
correct response at the last cor rectly recalled sequence length.
Results
T he m emor y sp an data were subjected to a two-way AN OVA in wh ich condition (con trol,
articulatory su ppression , or spatial tapping) and item (num erals or digit words) were
within-subjects factor s (see F igu re 5). T he results indicated a reliable m ain effect of
condition , F(2, 70) = 55.07, p < .0001 , with the largest d igit span und er control
(6.57), followed by spatial tapping (5.91), an d then articu lator y suppression (5.00) conditions. T he differences between recall conditions were all reliable (all t > 4.22, p < .001).
T he main effect of item, F(1, 35) = 12.10, p < .01, with a larger span for num erals than
digit words (means = 5.96 and 5.69, respectively) and the interaction between the factor s,
F(2, 70) = 4.26, p < .05, were reliable.
An alysis of th e interaction by simple main effects indicated a difference across recall
condition for numerals, F(2, 70) = 22.47, p < .0001, and digit words, F(2, 70) = 35.04,
FIG. 5.
M ean memory span for numerals and digit words un der silent, articulatory su p pression, and sp atial
tapping cond ition s in Exp eriment 4. T he error bar s r epr esent stand ard deviations.
342
CHINCOTTA ET AL.
p < .0001. T he d ifferences across recall conditions were all signi® cant at both the nu meral
and digit word levels of the item factor (all t > 2.12, p < .05). A differen ce between
nu m eral an d digit word span was noted at the control, F(1, 35) = 4.723, p < .05 (means =
6.74 and 6.40, respectively) and ar ticulatory suppression , F(1, 35) = 18.61, p < .0001
(m eans = 5.26 and 4.75) levels of the condition factor, bu t not at the spatial tapping level,
F(1, 35) < 1 (m eans = 5.89 and 5.93, respectively).
Discussion
T he advantage for nu merals over digit words noted u nder control and articulator y suppression conditions was eliminated wh en perform ance was measured u nd er a concurrent
sp atial tapping secondary task. T he resu lts of Exp eriment 4 thus suggest that the spatial
compon ent of visuo- spatial working memory plays a crucial role in m ed iating the nu meral
advantage effect. It shou ld be noted that, despite having a gr eater effect on overall
perfor mance, articulatory suppression showed a larger nu meral advantage effect. T his
® nding is consistent with that of Exp eriment 1 and rules ou t both a gen eral load an d a
phon ological interpretation of the effect.
It could, of course, be argu ed that the spatial tap ping task im plicated the central
executive compon ent of working memor y. We ® nd this possibility unlikely, for two
reasons: F irst, wh ile it seem s reasonable to suggest that spatial tasks that require complex or random patter ns to be tapp ed overload the central executive, the present
tapping task consisted of the continuous tapping of four pegs in a clockwise direction.
U nder these circumstances, any executive load, if present, was likely to be m inimal.
Second, in Exp erim en t 1 (where the item s were also presented in the sam e location), a
concurren t random generation task did not abolish the num eral advantage. If the effect
of spatial tapping in abolishin g the num er al advan tage was due to inherent central
executive dem and s, a similar ou tcome under random generation might have been
expected, wh ich was not the case. At this stage, it is m ore parsimon ious to attribute
the elim in ation of the numeral advantage effect to a disruption of visuo-spatial working
memor y.
Exp eriment 5 examined wh ether the effect of spatial tapping in elim inating the
nu m eral advantage was a consequence of a speci® c disruption of the spatial compon ent
of working m em ory or a result of a more general interference of visuo-spatial sketchpad
functioning.
EXPERIMENT 5
T o dissociate the involvement of the visual and spatial compon ents of working m em ory, a
condition that has been dem on strated to interfere selectively with visual coding was
introd uced into the design , in add ition to those d escribed for Exp eriment 4. T he
D yn am ic Visu al N oise (DVN ) technique (see, e.g., Quinn & M cC on nell, 1996 , for a fuller
discussion of the effects of DVN on visual p rocessing) allows th e presentation of m aterial
within a display of ir relevant, sem antically uncodable, visual p atter ns, wh ich does not
place undue d em ands on attention as there is no consistent focal p oint in wh ich change
occurs.
THE NUMERAL ADVANTAGE EFFECT
343
Method
Subjects
T he subjects were 24 (14 female, 10 male) undergraduate students registered with the sam e
British univer sity wh o volunteered to participate in the experiment.
Materials and Procedure
A new set of materials was constructed according to the criteria described for Experiment 1. In the
present experiment, a visual interfer ence condition was added, four sequences at each length wer e
presented, and recall was prom pted by a computer-gener ated tone. T he spatial tapping board was
occluded from view by means of a screen. For the measurement of memory span under visual
interference, a ver sion of the DVN display (e.g. Qu inn & M cConnell, 1996) was recreated. In
the present ver sion of DVN , the computer screen was divided into 1200 individual squares, each
measuring 4 3 4 pixels. At the star t of the program 50% of the squares were randomly coloured in
black, and the remaining squares were wh ite. On ce the progr am was initiated, 10% of the squares
changed from black to wh ite or vice-versa every second at random. T he stimuli appeared in the
location represented schematically in F igure 6. An additional 0.25 was added to the m emor y span
score for each cor rect r esponse at the last cor rectly recalled sequence length. T he remaining procedur al details were as described for Experiment 4.
Results
T he m emor y sp an data were subjected to a two-way AN OVA in wh ich condition (con trol,
articulatory su ppression, visual noise, or sp atial tapping) and item (num erals or digit
words) were both within-subjects factor s (see F igure 7). T h is indicated a reliable m ain
effect of cond ition, F(3, 69) = 41.47, p < .0001, with m em ory sp an und er articu lator y
su pp ression (4.89) lower than u nder control (6.65), visual noise (6.77), spatial tapping,
6.43, all t > 8.01, p < .001, wh ich did not differ amon g them selves. T he m ain effect of
item was not reliable, F(1, 23) = 2.39 (m eans = nu merals 6.23, digit words 6.14), bu t the
interaction between the factor s was reliable, F(3, 69) = 5.22, p < .01.
A detailed analysis of the interaction by simple main effects showed a gr eater memor y
sp an for num erals than for digit words under control, F(1, 23) = 5.27, p < .05 (m eans = 6.78
and 6.51, resp ectively), articulator y suppression , F(1, 23) = 10.67, p < .01 (means = 5.08
FIG. 6.
A sch ematic static r epr esentation of the pr esen tation of stimu li within the dynamic visual noise (DVN )
condition in Experim ent 5. T he display measured 200 3 150 cm, and the dimension of each dot was 4 3 4
pixels. T he black/ white r ate of change was a r andom 120 dots per sec.
344
CHINCOTTA ET AL.
FIG. 7.
M ean memory span for numerals and digit words u nd er silent, articulatory suppr ession , visual noise,
and spatial tapp ing cond ition s in Experiment 5. T he err or bars represent st andard d eviations.
and 4.70, respectively), and visual interference, F(1, 23) = 4.49, p < .05 (means = 6.90 an d
6.64, respectively) conditions. A reliable item d ifference was also noted under spatial
tapping, F(1, 23) = 21.07, p < .0001. In this case, however, m em ory span for digit words
was gr eater than for num erals (m eans = 6.70 and 6.16, respectively).
Both nu meral, F(3, 69) = 18.72, p < .0001, and d igit word, F(3, 69) = 25.21, p < .0001,
sp an varied as a function of condition. F urther analysis using a t test ind icated that for
nu m erals all the con trasts were reliable, t $ 2.30, p < .05, with the excep tion of the
comparison between the control and dyn amic visual noise conditions (t = 0.63). In the
case of digit words, however, a reliable difference was noted between articulator y suppression and the rem ain ing conditions, t $ 6.68, p < .001, and no other contrasts were
reliable.
Discussion
T he ® ndings of Exp erim ent 5 th us indicated that spatial tapping had a deleterious an d
sp eci® c effect on nu meral span. In Exp erim ent 4, spatial tapping elim inated a nu meral
advantage, wh ereas in Exp eriment 5 a digit word advantage was noted under th e sam e
condition. G iven that the m aterial was presented in the sam e location in both experiments, a procedural variation in the sp atial tapping task is on e likely explanation for the
variation in ou tcome. In Exp erim ent 4, the tapping board was placed 50 cm to on e side of
THE NUMERAL ADVANTAGE EFFECT
345
the m on itor an d was, therefore, peripherally visible, wh ereas in Exp erim ent 5 the board
was occluded from view by m eans of a screen. It is reasonable to suggest that the demands
on spatial processin g are likely to be gr eater under conditions wh ere the tapping board is
unseen than wh en it is partially visible.
A plausible explan ation for th e reversal of th e num eral advantage in Exp erim ent 5,
then, is that the occluded version of the spatial tapp ing secondary task occasion ed a mor e
deleterious degree of disru ption than did the unoccluded version. T his ubiquitou s disruption of visuo-spatial working m emory m ay have placed im por tant restrictions on the
use of visual codes that m ay be available under conditions in wh ich the spatial rehearsal
system is selectively disrupted. U nder such circum stances, novel processing str ategies
would be needed to cope with the processing dem ands of the m emor y task. If the visuosp atial system is m or e imp licated in the processing of num erals than digit words, then it is
reasonable to suggest that memor y span for the for mer would suffer disp rop or tionately
compared to the latter.
T his explanation of the reversal of the nu m eral advantage under spatial tapping in
Exp eriment 5 might appear somewhat contrived , bu t the results of a study that exam ined
a related effect converges with the present ® nd ings and increases the level of con® den ce in
the above interpretation . Chincotta and Jarrold (in p rep.) app lied th e sam e techniques
repor ted in this paper to an investigation of the character advantage effect: th e ® nding
that m em ory span for letters (e.g. j, i, u) is gr eater th an for words (e.g. jay, eye, you). T he
results are entirely consistent with the present ® ndings and dem on strate that an unocclu ded spatial tapping task abolishes th e mem ory span advan tage for letters over words
wh en the items are presented in the same location.
EXPERIMENT 6
T he ® nal experim ent examined wh ether the ® nding that a disr up tion of the spatial
rehearsal processes in visuo-sp atial workin g m em ory abolishes the memor y span su periority for nu merals over digit words could be extended to a presentation for mat in
wh ich the item s appeared in an ordered fashion within a 3 3
3 matrix (as in
Exp eriment 2).
Method
Subjects
T he subjects were 40 (20 female, 20 male) science undergr aduate students registered with the
same British university; they were paid for participation.
Materials and Procedure
T he materials and procedur al details for Experiment 6 were identical to those described for
Experiment 5, with the following exceptions. In the pr esent experiment, the stimuli were presented
within a 3 3 3 matrix as described for the ordered condition in Experiment 2, and the spatial tapping
task was as described in Experiment 4.
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CHINCOTTA ET AL.
Results
T he mem ory span data were subjected to a cor responding AN OVA (see F igure 8). T his
sh owed a reliable main effect of condition, F(3, 117) = 59.74, p < .0001, with memor y
sp an under articulatory suppression (5.73) lower th an under con trol (7.61), visual noise
(7.59), and spatial tap pin g (7.31, all t > 9.61, p < .001), wh ich did not differ amon g
themselves. A reliable m ain effect of item was also noted, F(1, 39) = 40.50, p < .0001,
with a larger numeral than digit word span (m eans = 7.30 an d 6.82, respectively). T he
interaction between the factor s was not reliable, F(3, 117) = 1.72, p > .05.
Althou gh th e absence of a reliable two-way interaction indicated that non e of the
secondary tasks abolish ed the nu meral advantage, this statistical suggestion was assessed
with a series of planned or th ogonal com parisons using a t-test. T he results con® rm ed that
a numeral advantage was noted under each condition (all t $ 2.32, p < .01).
Discussion
T he ® ndings of Exp erim ent 6 were str aightforward. T he absence of an interaction
between item and condition indicates a numeral advantage under all con ditions. T hus,
wh en the items were presented in an ordered , pred ictable fashion within a m atrix, neither
sp atial tapping nor visu al interference had any effect on mem ory span for nu m erals or
digit words, or the relationship between the items.
FIG. 8.
M ean memory span for numerals and digit words u nd er silent, articulatory suppr ession , visual noise,
and spatial tapp ing cond ition s in Experiment 6. T he err or bars represent st andard d eviations.
THE NUMERAL ADVANTAGE EFFECT
347
T hese p resent ® ndings are to be compared with those of Exp erim ent 5, in wh ich the
item s were presented in the same location and the numeral advantage was reversed under
sp atial tapping. It shou ld also be noted that both nu meral and digit word spans were
systematically higher (by approxim ately 1 item ) in Exp eriment 6 than in Exp erim en t 5.
T his patter n of ® ndings converges with th e evidence from Exp eriments 1±3 in that they
indicate that a predictable spatial distribution of the material provides robust exter nal
su pp lem en tary cues, wh ich im pr ove p erfor mance on th e on e hand and allow the visuosp atial system to resist the disruption of the spatial reh earsal compon ent on the other.
GENERAL DISCUSSION
T he ® nding that m em or y capacity for nu merals is greater than for digit word s repor ted by
Chincotta and U nderwood (1997a) was replicated in the six experim ents p resented here
and with a difference between the stimuli ranging from 0.27 un its (Exp eriment 6) to 0.54
units (Experim ent 3). T he num er al advan tage effect, alth ou gh small, was thus shown to
be robu st. T he impor tance of the present ® ndings, h owever, lay in the d em on stration of
an underlying difference in the processes that mediate serial recall between num erals an d
digit words. T h ese ® ndings stron gly suggest that nu meral stimuli enjoy an additional
source of suppor t in imm ediate serial recall tasks th at is unavailable for digit words.
H aving identi® ed these perform ance differen ces, how could their precise nature be interpreted in ter m s of a th eoretical framework?
T he results of Exp eriment 1 indicated that althou gh nu merals were identi® ed faster
than were digit words, respon se latency was not related to m em ory span. T hese ® ndings
thus did not converge with those of previous studies that have d em on strated an association between naming latency and m emory span (e.g. D empster, 1981). On e explan ation
for the different ou tcome of th e studies was that different par ad igm s were used to
measu re item identi® cation. N aming speed necessarily requires the activation of neural
plans for the execution of articulatory gestures, wh ereas the cross-mod al m atchin g task
used in Exp erim ent 1 obviated the need for articulation and m easured the speed of
respon se in recognizing the relationship between two stimuli as being the sam e or different. It could be argu ed, therefore, that th e absence of an association between respon se
latency and mem or y span in Exp erim ent 1 suggests that previous results m ay re¯ ect
sp eech prod uction processes rather than identi® cation processes p er se.
An alter native explanation is that th e m atching task lacked sensitivity to the factor s
that mediate item identi® cationÐ an issue that was addressed in Exp erim ents 2 and 3.
T he ® ndin gs indicated th at unpred ictable and unfamiliar presentation conditions
designed to d im inish the stren gth of associative links between items elim inated the
nu m eral advantage. T aken together, these ® ndings suggest th at the notion that the
cross-mod al m atch ing task was insensitive to factor s related to item identi® cation lacks
plausibility. For if the superior span for nu merals is deter m ined by su ch factor s alone,
random presentation (Exp erim ent 2) and an un fam iliar d irection of presentation (Exp eriment 3) would n ot have abolished the num eral advan tage effect.
T he ® nding that a disruption of the familiar patter ns in wh ich numerals are encountered in everyday life removed the nu m er al advantage provided an initial suggestion that
the effect was m od ulated by associative visual conn ections between these stimuli. T hese
348
CHINCOTTA ET AL.
® ndings were also consistent with th e notion that the nu meral advantage effect was
deter m ined by implicit or autom atic factor s and converged with the ® nding that the effect
was imperviou s to the effects of concurrent random gener ation (Exp erim ent 1). It seems
reasonable to suggest that the involvement of th e central execu tive in reorganizing material into more memor able codes m ay be limited to conditions in wh ich such strategies are
explicitly engaged and conscious effort is m ade.
At this point, two separate explanations of the numeral advan tage effect seemed plausible. On th e on e hand, the evidence from Exp erim ents 2 and 3 suggested that visual
associations between nu m erals and reading patter ns were an in¯ uential factor. T he ® nding
of a nu m er al advantage wh en the material was presented in the same location, however,
raised som e dou bt about the relevance of the spatial fam iliarity hypothesis as visual
patter ns and associations are not ger mane under these circum stances. O n the other
hand, the eviden ce from a nu mber of paradigms indicated that eye movements (e.g.
An drade et al., 1997; Idzikowski et al., 1983), su ch as those required in Exp erim ent 2
and 3, disrupted the visuo- spatial working memor y system.
H aving discounted the contribution of the ph on ological loop and central executive
compon ents of working memor y in mediating the num eral advantage effect, a logical next
step was to examine the involvement of the visuo- spatial sketchpad. A prod uctive
approach to u nderstanding the characteristics of visuo- sp atial working mem ory has
been to use the basic structure of the phon ological loop as a starting-p oint with wh ich
to examine visuo- spatial sketchpad functioning. L ogie (1995) has suggested that the
sp atial compon ent of visuo- spatial working m emor y plays a role in m aintain ing traces
in the visual store. T hese visual traces are subject to decay and interference but are
maintained for lon ger periods by the renewing action of the spatial system (inner scribe).
T he ® nding that spatial tapping eliminated the d ifference between nu m erals and digit
words (Exp erim ent 4) strikingly demon strated that the visuo- spatial working memor y was
implicated in mediating the nu m eral advantage effect. Alth ou gh at this stage the elimination of th e nu meral advantage by spatial tapping could reasonably be attributed to a
disruption of the spatial comp on ent of the visuo- spatial sketchpad, Exp erim ent 5 was
designed to d issociate the relative involvem en t of the visual and spatial compon ents of
working mem ory. T his was achieved by introd ucing a cond ition th at selectively disrupts
visual codin g (D yn am ic Visual N oise, e.g. Q uin n & M cCon nell, 1996). T he ® ndings
indicated that visu al interference had no effect on the num eral advantage, wh ereas an
occluded spatial tapping task reversed the effect in favour of digit word s. M or e im por tant,
however, this ® nding con® r ms that spatial tapping d oes not occasion a gen eral curtailm ent
of the visu o-spatial mem or y bu t, rather, a selective d isruption of the spatial comp on ent.
Based on L ogie’s (1995) mod i® ed mod el of the visuo-spatial sketchpad, on e logical
interp retation of the removal of a nu meral advantage by spatial tapping is that the refreshing action of the spatial system in visual m emor y plays a crucial role in m ediating the
effect. Ar abic numerals use fewer visual features to convey the same in for m ation than do
digit words and thu s are a mor e succinct, discriminable representation of digits. If a
tem por ary visual store of ® nite capacity is assumed, m emory span for items that occupy
fewer of the resources of the system is likely to be greater than for items that absorb mor e
of the available capacity. If the visuo-spatial working memor y sytem is seen as br oadly
analogous to the phon ological loop, on e explanation of the num eral advantage effect,
THE NUMERAL ADVANTAGE EFFECT
349
therefore, is that numerals and digit words make differential demand s on the capacity of
the visuo- sp atial memor y system : a typ e of visual word-length effect.
If, however, the difference in m em ory span between num erals and d igit words was
wh olly mediated by a simple version of a visu al word-length effect, a greater im pair m ent
might be expected for digit word mem ory span as a few of th ese item s would be likely to
consume the available visual capacity. A m ore reasonable explanation, therefore, is that the
nu m eral advantage effect is m ediated, not so much by visual capacity lim itations per se,
bu t by a variation in the ef® ciency with wh ich the discrete rep resentations of digits are
maintained with in the visual stor e throu gh the refresh ing action of th e sp atial rehearsal
system. By exten sion, this accoun t similarly attributes the abolition of the num eral
advantage under random and unfam iliar spatial distribution s to an equ ivalent disru ptive
effect of eye m ovements on the fu nctionin g of the spatial rehear sal system .
T he ® nd ing of a scanning or der effect (Exp eriment 3) is suggestive of a link with
reading habit and ind icates that the nu m eral advan tage effect is partly d ependent upon
extensive prior lear ning. In add ition, the ® nding that the ordered presentation of m aterial
within a grid both increased overall m emory span by approximately 1 item and engendered an im mu nity to the effect of a disruption of the spatial rehearsal process suggests
that the nu m eral advantage effect is u nlikely to be exclusively mod erated by a single
factor. Instead , it seems mor e plausible that th e effect is occasioned by multi-compon ent
processes involving visu al length, familiarity, and, possibly, implicit for m s of chunkin g.
Althou gh an answer to these issues lay beyond the scope of the present study, on e
® nding was clear. T he num eral advantage effect qu estions th e assum ption that the pr ocesses underlying serial recall are equivalent between categories. T he present ® ndings
sh ow that the variation in visu al m emor y span between num erals and digit words is
mediated by factor s other than articu lation tim e, item iden ti® cation tim e, and the strength
of long-ter m m emory representation s for individual item s. Instead, the numeral advantage effect may be partly exp lained in ter m s of capacity lim itations of the visual stor e, the
ef® ciency of the spatial rehearsal system, and lon g-ter m kn owledge of the visual associations between the item s. N ot least, the present ® ndings provide further evidence for the
presence of a visual component of working memor y an d its role in the processing of
visually pr esented verbal m aterial.
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Original manuscript received 22 September 1997
Accepted revision receiv ed 6 April 1998